CACmb/src/opt_disl.f90

module opt_disl

    !This module contains all code associated with dislocations

    use parameters
    use elements
    use subroutines
    use box 
    implicit none


    real(kind=dp), dimension(3) :: line, slip_plane, centroid!dislocation line, slip plane vectors, centroid,
    real(kind=dp) ::  burgers(3)  !burgers vector of loop
    real(kind=dp) :: poisson, char_angle, lattice_parameter!Poisson ratio and character angle, lattice_parameter for burgers vector
    character(len=10) :: lattice
    character(len=1) :: loop_normal
    real(kind=dp) :: loop_radius !Dislocation loop radius
    
    real(kind=dp) :: b !burgers vector


    public 
    contains 

    subroutine dislocation(option, arg_pos)

        !Main calling function for all codes related to dislocations

        character(len=100), intent(in) :: option
        integer, intent(inout) :: arg_pos 


        select case(trim(adjustl(option)))
        case('-dislgen')
            call parse_dislgen(arg_pos)
            call dislgen
        case('-disloop')
            call parse_disloop(arg_pos)
            call disloop
        end select
    end subroutine dislocation

    subroutine parse_dislgen(arg_pos)

        !Parse dislgen command

        integer, intent(inout) :: arg_pos

        integer :: i,arglen
        character(len=8) :: ori_string
        character(len=100) :: textholder

        !Parse all of the commands
        arg_pos = arg_pos + 1
        line(:) = 0.0_dp
        call get_command_argument(arg_pos, ori_string, arglen)
        if (arglen==0) STOP "Missing line vector in dislgen command"
        call parse_ori_vec(ori_string, line)

        arg_pos=arg_pos + 1
        slip_plane(:) = 0.0_dp
        call get_command_argument(arg_pos, ori_string, arglen)
        if (arglen==0) STOP "Missing plane vector in dislgen command"
        call parse_ori_vec(ori_string, slip_plane)

        do i = 1, 3
            arg_pos = arg_pos + 1
            call get_command_argument(arg_pos, textholder, arglen)
            if (arglen==0) STOP "Missing centroid in dislgen command"
            call parse_pos(i, textholder, centroid(i))           
        end do

        arg_pos = arg_pos + 1
        call get_command_argument(arg_pos, textholder, arglen)
        if (arglen==0) STOP "Missing parameter in dislgen command"
        read(textholder, *) b 


        arg_pos = arg_pos + 1
        call get_command_argument(arg_pos, textholder, arglen)
        if (arglen==0) STOP "Missing character angle in dislgen command"
        read(textholder, *) char_angle


        arg_pos = arg_pos + 1
        call get_command_argument(arg_pos, textholder, arglen)
        if (arglen==0) STOP "Missing poisson in dislgen command"
        read(textholder, *) poisson

        arg_pos = arg_pos + 1
    end subroutine parse_dislgen

    subroutine dislgen
        !This subroutine creates the actual dislocation

        integer :: i, sub_box, inod, ibasis
        real(kind=dp) :: ss_ori(3,3), ss_inv(3,3), be, bs, slipx(3), disp_transform(3,3), inv_transform(3,3), &
                         actan, r(3), disp(3)

        !Calculate screw and edge burgers vectors
        be = sin(char_angle*pi/180.0_dp)*b
        bs = cos(char_angle*pi/180.0_dp)*b

        !Figure out which sub box you are in so you can access it's orientation, this code will not work
        !with overlapping sub_boxes
        do i = 1, sub_box_num
            if(in_block_bd(centroid, sub_box_bd(:,i))) then 
                sub_box = i
                exit
            end if
        end do

        !Construct the slip system orientation matrix in an unrotated system 
        slipx = cross_product(slip_plane, line)
        ss_ori(1,:) = unitvec(3,slipx)
        ss_ori(2,:) = unitvec(3,slip_plane)
        ss_ori(3,:) = unitvec(3,line)
        call matrix_inverse(ss_ori, 3, ss_inv)

        !Apply the rotation
        disp_transform = matmul(sub_box_ori(:,:,i), ss_inv)
        call matrix_inverse(disp_transform,3,inv_transform)

        if(atom_num > 0) then 
            do i = 1, atom_num
                r=r_atom(:,i) - centroid
                r=matmul(inv_transform, r)
                if (r(1) == 0) then 
                    actan=pi/2
                else
                    actan = datan2(r(2),r(1))
                end if

                if ((r(1)**2 + r(2)**2) == 0) cycle

                !This is the elastic displacement field for dislocation according to Hirth and Lowe
                disp(1) = be/(2.0_dp*pi) * (actan + (r(1)*r(2))/(2.0_dp*(1.0_dp-poisson)*(r(1)**2.0_dp + r(2)**2.0_dp)))
                disp(2) = -be/(2.0_dp*pi)*((1.0_dp-2.0_dp*poisson)/(4.0_dp-4.0_dp*poisson) * &
                                            log(r(1)**2.0_dp + r(2)**2.0_dp) &
                                            + (r(1)**2.0_dp - r(2)**2.0_dp)/(4.0_dp*(1.0_dp-poisson)&
                                            *(r(1)**2.0_dp+r(2)**2.0_dp)))
                disp(3) = bs/(2.0_dp*pi) * actan

                !This transforms the displacement to the correct orientation
                disp = matmul(disp_transform, disp)

                r_atom(:,i) = r_atom(:,i) + disp
            end do
        end if

        if(ele_num > 0) then 
            do i = 1, ele_num
                do inod=1, ng_node(lat_ele(i))
                    do ibasis = 1, basisnum(lat_ele(i))
                        r = r_node(:,ibasis,inod,i)-centroid
                        r = matmul(inv_transform, r)
                        if (r(1) == 0) then 
                            actan = pi/2
                        else
                            actan = datan2(r(2),r(1))
                        end if

                        if ((r(1)**2 + r(2)**2) == 0) cycle
                
                        !This is the elastic displacement field for dislocation according to Hirth and Lowe
                        disp(1) = be/(2.0_dp*pi) * (actan + (r(1)*r(2))/(2.0_dp*(1.0_dp-poisson)*(r(1)**2.0_dp + r(2)**2.0_dp)))
                        disp(2) = -be/(2.0_dp*pi)*((1.0_dp-2.0_dp*poisson)/(4.0_dp-4.0_dp*poisson) * &
                                                    log(r(1)**2.0_dp + r(2)**2.0_dp) &
                                                    + (r(1)**2.0_dp - r(2)**2.0_dp)/(4.0_dp*(1.0_dp-poisson)&
                                                    *(r(1)**2.0_dp+r(2)**2.0_dp)))
                        disp(3) = bs/(2.0_dp*pi) * actan


                        disp = matmul(disp_transform, disp)
                        r_node(:,ibasis,inod,i) = r_node(:,ibasis,inod,i) + disp
                    end do
                end do
            end do
        end if

    end subroutine dislgen

    subroutine parse_disloop(arg_pos)
        !This subroutine parses the disloop command

        integer, intent(inout) :: arg_pos

        integer :: i,arglen, sbox
        character(len=8) :: ori_string
        character(len=100) :: textholder

        !Parse all of the commands
        arg_pos = arg_pos + 1
        loop_normal = ' '
        call get_command_argument(arg_pos, loop_normal, arglen)
        if (arglen==0) STOP "Missing loop_normal in disloop command"
        !Convert the loop_normal to the dimension
        select case(loop_normal)
            case('x','X', 'y', 'Y', 'z', 'Z')
               continue
            case default
                print *, "Dimension argument must either be x, y, or z not", loop_normal
                stop 3
        end select

        arg_pos = arg_pos + 1
        loop_radius = 0
        call get_command_argument(arg_pos, textholder, arglen)
        if (arglen==0) STOP "Missing loop_size in disloop command"
        read(textholder, *) loop_radius

        do i = 1, 3
            arg_pos = arg_pos + 1
            call get_command_argument(arg_pos, textholder, arglen)
            if (arglen==0) STOP "Missing centroid in disloop command"
            call parse_pos(i, textholder, centroid(i))           
        end do

        burgers(:) = 0.0_dp
        do i = 1, 3
            arg_pos = arg_pos + 1
            call get_command_argument(arg_pos, textholder, arglen)
            if (arglen==0) STOP "Missing burgers vector in disloop command"
            read(textholder, *) burgers(i)
        end do

        arg_pos = arg_pos + 1
        call get_command_argument(arg_pos, textholder, arglen)
        if (arglen==0) STOP "Missing poisson ratio in disloop command"
        read(textholder, *) poisson

        arg_pos = arg_pos + 1

        !Now check to make sure that the dimension selected is actually a 1 1 1 direction.
        ! call in_sub_box(centroid, sbox)
        ! if(.not.((abs(sub_box_ori(loop_normal,1,sbox)) == abs(sub_box_ori(loop_normal,2,sbox))).and. &
        !          (abs(sub_box_ori(loop_normal,2,sbox)) == abs(sub_box_ori(loop_normal,3,sbox))).and. &
        !          (abs(sub_box_ori(loop_normal,3,sbox)) == abs(sub_box_ori(loop_normal,1,sbox))))) then 

        !     print *, "The selected dimension ", loop_normal, " for sub_box ", sbox, " is ", &
        !              sub_box_ori(loop_normal,:,sbox), " which is not in the (111) family of planes"
        !     STOP 3 
        ! end if


    end subroutine

    !Code for the creation of dislocation loops is based on functions from atomsk
    !which is available from https://atomsk.univ-lille.fr/. They have been adapted to fit cacmb.
    subroutine disloop
        !This subroutine applies the displacement field for a dislocation loop to all atoms and elements.
        integer :: a1, a2, a3 !New directions
        integer :: i, j, inod, ibasis, Npoints 
        real(kind = dp) :: perimeter, angle, theta, omega, xA(3), xB(3), xC(3), u(3)
        real(kind=dp), dimension(:,:), allocatable :: xloop !coordinate of points forming loop

        if(allocated(xLoop)) deallocate(xLoop)

        !Define new directions
        select case(loop_normal)
        case('x','X')
            !Loop in (y,z) plane
            a1 = 2
            a2 = 3
            a3 = 1
        case('y','Y')
            !Loop in (x,z) plane
            a1 = 3
            a2 = 1
            a3 = 2
        case default
            !Loop in (x,y) plane
            a1 = 1
            a2 = 2
            a3 = 3
        end select

        if(loop_radius < 0.0_dp) then 
                ALLOCATE(xLoop(4,3))
                xLoop(:,:) = 0.d0
                xLoop(1,a1) = centroid(1) - loop_radius
                xLoop(1,a2) = centroid(2) - loop_radius
                xLoop(1,a3) = centroid(3)
                 xLoop(2,a1) = centroid(1) + loop_radius
                 xLoop(2,a2) = centroid(2) - loop_radius
                 xLoop(2,a3) = centroid(3)
                xLoop(3,a1) = centroid(1) + loop_radius
                xLoop(3,a2) = centroid(2) + loop_radius
                xLoop(3,a3) = centroid(3)
                 xLoop(4,a1) = centroid(1) - loop_radius
                 xLoop(4,a2) = centroid(2) + loop_radius
                 xLoop(4,a3) = centroid(3)
        else
            !Calculate loop perimeter
            perimeter = 2.0_dp*pi*loop_radius

            !Define the number of points forming the loop 
            ! The following criteria are used as a trade-off between
            ! good accuracy and computational efficiency:
            ! - each dislocation segment should have a length of 5 angströms;
            ! - the loop should contain at least 3 points
            !    (for very small loops, this will result in segments shorter than 5 A);
            ! - there should not be more than 100 points
            !    (for very large loops, this will result in segments longer than 5 A).
            Npoints = MAX( 3 , MIN( NINT(perimeter/5.d0) , 100 ) )

            !angle between two consecutive points
            theta = 2.0_dp*pi / dble(Npoints)

            !allocate xLoop
            allocate(xLoop(Npoints,3))
            xLoop(:,:) = 0.0_dp

            !Calculate the position of each point in the loop
            angle = 0.0_dp
            do i = 1, size(xLoop,1)
                xLoop(i,a1) = centroid(a1) + loop_radius*dcos(angle)
                xLoop(i,a2) = centroid(a2) + loop_radius*dsin(angle)
                xLoop(i,a3) = centroid(a3)
                ! Increment angle for next point
                angle = angle + theta
            end do
        end if
        !Now actually calculate the displacement created by a loop for every atom
        do i = 1, atom_num
            u = 0.0_dp
            omega = 0.0_dp
            xC(:) = centroid - r_atom(:,i)

            !Loop over all dislocation segments
            do j = 1, size(xLoop,1)
                !Coordinates of point A
                if (j ==1) then
                    xA(:) = xLoop(size(xLoop,1),:) - r_atom(:,i)
                else
                    xA(:) = xLoop(j-1, :) - r_atom(:,i)
                end if

                !Coordinates of point B
                xB(:) = xLoop(j,:) - r_atom(:,i)

                !Displacement due to solid angle
                omega = omega + SolidAngle(xA, xB, xC)
                !Displacement due to elasticity
                u(:) = u(:) + DisloSeg_displacement_iso(xA, xB, burgers(:), poisson)
            end do

            !Total displacement
            u=u(:) + burgers(:) * omega

            !Apply displacement to atom
            r_atom(:,i) = r_atom(:,i) + u(:)
        end do

        !Repeat for element nodes
        do i = 1, ele_num
            do inod =1, ng_node(lat_ele(i))
                do ibasis = 1, basisnum(lat_ele(i))
                    u = 0.0_dp
                    omega = 0.0_dp
                    xC(:) = centroid - r_node(:,ibasis,inod,i)

                    !Loop over all dislocation segments
                    do j = 1, size(xLoop,1)
                        !Coordinates of point A
                        if (j ==1) then
                            xA(:) = xLoop(size(xLoop,1),:) - r_node(:,ibasis,inod,i)
                        else
                            xA(:) = xLoop(j-1, :) - r_node(:,ibasis,inod,i)
                        end if

                        !Coordinates of point B
                        xB(:) = xLoop(j,:) - r_node(:,ibasis,inod,i)

                        !Displacement due to solid angle
                        omega = omega + SolidAngle(xA, xB, xC)
                        !Displacement due to elasticity
                        u(:) = u(:) + DisloSeg_displacement_iso(xA, xB, burgers(:), poisson)
                    end do

                    !Total displacement
                    u=u(:) + burgers(:) * omega

                    !Apply displacement to atom
                    r_node(:,ibasis,inod,i) = r_node(:,ibasis,inod,i) + u(:)
                end do
            end do 
        end do
        return
    end subroutine

    !********************************************************
    ! SOLIDANGLE
    ! Calculate solid angle (normalized by 4*pi) used to obtain the 
    ! displacement created by a dislocation triangle loop ABC at the origin
    ! (field point = origin)
    ! Ref.: Van Oosterom, A. and Strackee, J., 
    !       The Solid Angle of a Plane Triangle, 
    !       IEEE Transactions on Biomedical Engineering BME-30, 125 (1983).
    !********************************************************
    FUNCTION SolidAngle(xA, xB, xC) RESULT(Omega)
    !
    IMPLICIT NONE
    !
    ! Extremities of the triangle loop
    REAL(dp),DIMENSION(3),INTENT(IN) :: xA, xB, xC
    !
    ! Solid angle (normalized by 4*pi)
    REAL(dp):: omega
    REAL(dp),PARAMETER:: factor=1.d0/(2.d0*pi)
    !
    REAL(dp) :: rA, rB, rC, numerator, denominator
    !
    rA = norm2(xA)
    rB = norm2(xB)
    rC = norm2(xC)
    !
    numerator = TRIPLE_PRODUCT( xA, xB, xC )
    denominator = rA*rB*rC + DOT_PRODUCT( xA, xB )*rC &
                & + DOT_PRODUCT( xB, xC )*rA + DOT_PRODUCT( xC, xA )*rB
    !
    omega = factor*ATAN2( numerator, denominator )
    !
    END FUNCTION SolidAngle

    !********************************************************
    ! DISLOSEG_DISPLACEMENT_ISO
    ! Calculate displacement created by dislocation segment AB
    ! once the solid angle part has been removed
    ! Isotropic elastic calculation with nu Poisson coef.
    ! Ref.: Eq. (1) in Barnett, D. M. 
    !       The Displacement Field of a Triangular Dislocation Loop
    !       Philos. Mag. A, 1985, 51, 383-387 
    !********************************************************
    FUNCTION DisloSeg_displacement_iso(xA, xB, b, nu) RESULT(u)
    !
    IMPLICIT NONE
    REAL(dp),DIMENSION(3),INTENT(IN):: xA, xB ! Extremities of the segment
    REAL(dp),DIMENSION(3),INTENT(IN):: b  ! Burgers vector
    REAL(dp),INTENT(IN):: nu    ! Poisson coefficient
    REAL(dp),DIMENSION(3):: u ! Displacement
    REAL(dp):: rA, rB
    REAL(dp),DIMENSION(1:3)::  tAB, nAB 
    !
    rA = norm2(xA)
    rB = norm2(xB)
    !
    ! Tangent vector
    tAB(:) = xB(:) - xA(:)
    tAB(:) = tAB(:)/norm2(tAB)
    !
    ! Normal vector
    nAB(:) = CROSS_PRODUCT(xA,xB)
    nAB(:) = nAB(:)/norm2(nAB)
    !
    u(:) = ( -(1.d0-2.d0*nu)*CROSS_PRODUCT(b, tAB)* &
         &  LOG( (rB + DOT_PRODUCT(xB,tAB))/(rA + DOT_PRODUCT(xA,tAB)) ) &
         &  + DOT_PRODUCT(b,nAB)*CROSS_PRODUCT(xB/rB-xA/rA,nAB) ) &
         &  /(8.d0*pi*(1.d0-nu))
    !
    END FUNCTION DisloSeg_displacement_iso
!
    !This code simply creates a planar vacancy cluster and does not apply the dislocation loop displacement field.
    ! subroutine disloop
    !     !This subroutine actually creates the dislocation loop.

    !     real(kind=dp) :: neighbor_dis(loop_size), temp_box(6), dis
    !     integer :: i, j, index(loop_size)

    !     neighbor_dis(:) = HUGE(1.0_dp)
    !     index(:) = 0

    !     !First find the nearest atom to the centroid 
    !     do i = 1, atom_num
    !         if(norm2(r_atom(:,i) - centroid) < neighbor_dis(1)) then 
    !             neighbor_dis(1) = norm2(r_atom(:,i) - centroid)
    !             index(1) = i
    !         end if
    !     end do 

    !     !Define a new box, this box tries to isolate all atoms on the plane of the atom 
    !     !closest to the user defined centroid.
    !     temp_box(:) = box_bd(:) 
    !     temp_box(2*loop_normal) = r_atom(loop_normal,index(1)) + 10.0_dp**(-2.0_dp)
    !     temp_box(2*loop_normal-1) = r_atom(loop_normal,index(1)) - 10.0_dp**(-2.0_dp)

    !     !Now reset the list for the scanning algorithm
    !     index(1) = 0
    !     neighbor_dis(1) = HUGE(1.0_dp)

    !     !Now scan over all atoms again and find the closest loop_size number of atoms to the initial atom 
    !     !that reside on the same plane.

    !     do i = 1, atom_num
    !         !Check to see if it is on the same plane
    !         if (in_block_bd(r_atom(:,i), temp_box)) then 
    !             dis = norm2(r_atom(:,i) - centroid)
    !             do j = 1, loop_size
    !                 !Check to see if it is closer than other atoms
    !                 if (dis < neighbor_dis(j)) then 
    !                     !Move values in the neighbor array and add the new neighbor
    !                     if(j < loop_size) then 
    !                         neighbor_dis(j+1:loop_size) = neighbor_dis(j:loop_size-1)
    !                         index(j+1:loop_size) = index(j:loop_size-1)
    !                     end if
    !                     neighbor_dis(j) = dis
    !                     index(j) = i
    !                     exit
    !                 end if
    !             end do 
    !         end if
    !     end do 

    !     !Now delete the atoms
    !     call delete_atoms(loop_size, index)

    !     return
    ! end subroutine disloop

end module opt_disl